The area of a sector is 18π cm2, and its radius is 6 cm. What is the central angle (in radians)?
\(\pi\)
Area of a sector with central angle \(\theta\) (in radians) \(= \frac{1}{2} r^2 \theta\).
\(\frac{1}{2} \times 6^2 \times \theta = 18\pi \Rightarrow 18\theta = 18\pi\)
\(\theta = \pi\) radians (that is, 180°, a semicircle).
Hence, the central angle is \(\pi\) radians.
Similar Questions
A circular garden has radius 10 m. What is its area in square meters?
A circular sheet of radius 10 cm is cut to form a sector of 120°. What is the length of the arc of this sector?
A rectangle of side 8 cm × 6 cm and a rhombus (side = 8 cm, acute angle 60°) are joined along one 8 cm side. What's the ratio of their areas (rectangle : rhombus)?
A trapezium has height 10 cm and area 180 cm2. If one parallel side is 12 cm, what is the other side?
Important Questions from 2-D Mensuration
- The length of a rectangular plot is $(x^2 + xy + y^2)$ m and its breadth is $(x^2 - 5xy - y^2)$ m.
Find its perimeter, when $x = 1$ and $y = -1$. - The ratio between the perimeter and breadth of a rectangle is 3: 1. If the area of the rectangle is $98 \text{ cm}^2$, find the perimeter (in cm) of the rectangle.
The shorter side of a rectangle is 15 cm less than the longer side. The numerical value of its area is equal to 5 times the numerical value of its perimeter. What is the length (in cm) of its longer side?
- In a circle of radius 10.5 cm, if the angle of a sector is $\frac{2\pi}{3}$, then the perimeter of the sector is (in cm):
(Take $\pi = \frac{22}{7}$) - Find the circumference (in m) of the largest circle that can be inscribed in a rectangle whose dimensions are given as 114 m and 63 m.
Take $\pi = \frac{22}{7}$
